前人研究已證實，具備宇稱－時間（PT）對稱之非厄米哈密頓量在淬滅動力
學中會因能級交叉而產生糾纏轉變。本論文系統性地運用雙正交右–左（R-L）
基底，深入探討PT對稱非厄米淬滅動力學中糾纏熵、物理可觀測量與量子幾何
的演化行為。研究結果揭示自由費米子系統與交互作用費米子系統之間的本質
差異：
1. 自由系統
約化密度矩陣保持高斯形式，並可分解為相互解耦的2×2 子空間，導致本
徵值呈譜配對（spectral pairing），使糾纏熵隨時間線性增長。
2. 交互作用系統
交互作用破壞了上述對稱性。透過微擾分析，我們發現交互作用誘導的四
次項耦合了先前獨立的模態，將有效子空間擴展至4×4，因而使糾纏熵呈
指數增長。
此外，本論文並透過對Yang-Lee mode 和非厄米Su–Schrieffer–Heeger (SSH)
modell 的詳細研究，進一步佐證上述發現，從而建立非厄米淬滅動力學、糾纏
尺度行為與相變之間的直接關聯。這些發現凸顯了譜結構在主導糾纏動力學中
的關鍵作用，並為深入理解交互作用、對稱破缺與非厄米多體系統行為間的相
互影響提供了新的視角。

Previous studies have demonstrated that the quench dynamics of parity-time
(PT)-symmetric non-Hermitian Hamiltonians exhibit entanglement transitions drivenby level crossings. In this thesis, we extend these analyses by systematically investigating the evolution of entanglement entropy, physical observables, and quantum geometry in PT-symmetric non-Hermitian quench dynamics using the biorthogonal right–left (R-L) basis. Our results reveal a fundamental distinction between free and interacting fermionic systems. In free systems, the reduced density matrix retains a Gaussian form that factorizes into decoupled 2 × 2 subspaces, resulting in a spectral pairing of eigenvalues that yields a linear time growth of entanglement entropy. In contrast, the introduction of interactions breaks this symmetry. Through a perturbative analysis, we demonstrate that the interaction-induced quartic terms couple previously independent modes, enlarging the effective sub-space to 4 × 4 and leading to an exponential increase in entanglement entropy. We corroborate these findings through detailed studies on the Yang–Lee modeland the non-Hermitian Su–Schrieffer–Heeger (SSH) model, thereby establishing a direct link between non-Hermitian quench dynamics, entanglement scaling, and phase transitions. These insights underscore the pivotal role of spectral structure in governing entanglement dynamics and provide a deeper understanding of the interplay between interactions, symmetry breaking, and the behavior of non-Hermitian many-body systems.